Mathematics > Algebraic Geometry

Title:The motivic Steenrod algebra in positive characteristic

Abstract: Let S be an essentially smooth scheme over a field and l a prime number
invertible on S. We show that the algebra of bistable operations in the mod l
motivic cohomology of smooth S-schemes is generated by the motivic Steenrod
operations. This was previously proved by Voevodsky for S a field of
characteristic zero. We follow Voevodsky's proof but remove its dependence on
characteristic zero by using étale cohomology instead of topological
realization and by replacing resolution of singularities with a theorem of
Gabber on alterations.